3,058 research outputs found
Sequential Dimensionality Reduction for Extracting Localized Features
Linear dimensionality reduction techniques are powerful tools for image
analysis as they allow the identification of important features in a data set.
In particular, nonnegative matrix factorization (NMF) has become very popular
as it is able to extract sparse, localized and easily interpretable features by
imposing an additive combination of nonnegative basis elements. Nonnegative
matrix underapproximation (NMU) is a closely related technique that has the
advantage to identify features sequentially. In this paper, we propose a
variant of NMU that is particularly well suited for image analysis as it
incorporates the spatial information, that is, it takes into account the fact
that neighboring pixels are more likely to be contained in the same features,
and favors the extraction of localized features by looking for sparse basis
elements. We show that our new approach competes favorably with comparable
state-of-the-art techniques on synthetic, facial and hyperspectral image data
sets.Comment: 24 pages, 12 figures. New numerical experiments on synthetic data
sets, discussion about the convergenc
Decorrelation of Neutral Vector Variables: Theory and Applications
In this paper, we propose novel strategies for neutral vector variable
decorrelation. Two fundamental invertible transformations, namely serial
nonlinear transformation and parallel nonlinear transformation, are proposed to
carry out the decorrelation. For a neutral vector variable, which is not
multivariate Gaussian distributed, the conventional principal component
analysis (PCA) cannot yield mutually independent scalar variables. With the two
proposed transformations, a highly negatively correlated neutral vector can be
transformed to a set of mutually independent scalar variables with the same
degrees of freedom. We also evaluate the decorrelation performances for the
vectors generated from a single Dirichlet distribution and a mixture of
Dirichlet distributions. The mutual independence is verified with the distance
correlation measurement. The advantages of the proposed decorrelation
strategies are intensively studied and demonstrated with synthesized data and
practical application evaluations
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